I have the following problem for homework:
Compute gcd(57,93), and find integers s and t such that 57s + 93t = gcd(57,93).

Now I have computed gcd(57,93) = 3 using the Extended Euclidean Algorithm. I am a bit lost on the second part of the question. I was wondering if somebody could help me start or lead me in the right direction as to how to solve the second part.

Dec 10th 2010, 06:12 PM

dwsmith

Can you take it from here?

Dec 10th 2010, 06:28 PM

tr6699

That is what I used to find the gcd. I don't really know what the second part is asking me to do, or how to do it.

Dec 10th 2010, 06:31 PM

dwsmith

Dec 10th 2010, 06:35 PM

tr6699

Not to sound ungrateful for you quick responses, but could you explain that a little. I don't really understand what you are doing there.

Dec 10th 2010, 06:43 PM

dwsmith

I am taking the GCD of 3 in the last equation and isolating it on one side of the equation. I then do the same for all the remainders. Then in each equation you will see, for instance, but above this we have . By substitution, we obtain . Then we simplify and continue to substitute.

Dec 10th 2010, 07:22 PM

tr6699

Okay, thank you very much for the clarification. I continued that and ended up with 3 = 8 X 93 - 13 X 57. Thus making s = -13 and t = 8.

Dec 11th 2010, 06:25 AM

HallsofIvy

The problem is to solve 57s + 93t = gcd(57,93)= 3. Divide both sides of the equation by 3 to get 19s+ 31t= 1